Work

The Least-Norm Solution to a Matrix Equation over the Dual Quaterion Algebra

Year: 2025

Type: article

Abstract: In this paper, we explore the least-norm solution to the classical matrix equation AXB=C over the dual quaternion algebra. We begin by transforming the definition of the Frobenius norm for dual quaternion matrices into an equivalent form. Using this new expression, we investigate the least-norm solution to the equation AXB=C under solvability conditions. Additionally, we examine the minimum real part of norm solution in cases where a least-norm solution does not exist. Finally, we provide two numerical examples to illustrate the main findings of our study.

Source: Symmetry

DOI: 10.3390/sym17020267

Authors: Ling-Jie Zhu, Qing-Wen Wang, Zu-Liang Kou

Institution: Shanghai University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: National Natural Science Foundation of China